[tex]\bf n^{th}\textit{ term of a geometric sequence}\\\\
a_n=a_1\cdot r^{n-1}\qquad
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
r=\textit{common ratio}\\
----------\\
r=\frac{1}{3}\\
n=5\\
a_5=\frac{1}{3}
\end{cases}\implies a_5=a_1\cdot \left( \frac{1}{3} \right)^{5-1}[/tex]
[tex]\bf \cfrac{1}{3}=a_1\cdot \left( \frac{1}{3} \right)^{5-1}\implies \cfrac{1}{3}=a_1\cdot \cfrac{1^4}{3^4}\implies \cfrac{1}{3}=\cfrac{a_1}{81}\implies \cfrac{81}{3}=a_1
\\\\\\
27=a_1\qquad \qquad thus\qquad \qquad \boxed{a_n=27 \left( \frac{1}{3} \right)^{n-1}}[/tex]
